Absolute Nodal Coordinate Formulation Based on Moving Least Square Method for Plane Flexible Beam

In engineering, flexible slender beams often encounter strong nonlinear large deformation problems, which will greatly hinder the precise control and lightweight optimization of flexible components. Therefore, a method that can accurately analyze the large deformation problem of flexible slender beams is needed.

In this paper, an Absolute Nodal Coordinate Formulation (ANCF) based on the Moving Least Squares (MLS), denoted as MANCF, is developed to deal with the large deformation problem of plane flexible slender beams accurately and efficiently. The MLS in the meshfree method does not need to divide the mesh, which can avoid the problems such as mesh distortion caused by mesh division. MLS can ensure the high-order continuity of its shape function through the basis function and the weight function, and ensure the continuity and accuracy of the beam curvature through the highly overlapping support domain.

In this paper, through three static cases and two dynamic cases, it is demonstrated that MANCF (Absolute Nodal Coordinate Formulation based on moving least square method) can obtain higher calculation accuracy and ensure the continuity of beam curvature compared with traditional ANCF in dealing with large deformation analysis of flexible beams. In addition, in dynamic problems, the results of MANCF are always better than those of traditional ANCF, and it also has good applicability to complex multi-body dynamic systems.

MANCF can effectively solve the drawbacks caused by meshing in traditional ANCF, and achieve higher accuracy while ensuring the continuity of beam curvature, which shows that MANCF has great potential in engineering problems.